TY - JOUR
T1 - Moments of claims in a Markovian environment
AU - Kim, Bara
AU - Kim, Hwa Sung
N1 - Funding Information:
We are very grateful to the referee and the editor, Rob Kaas, for valuable comments on this paper. This research was supported by the MIC (Ministry of Information and Communication), Korea, under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute of Information Technology Assessment).
Copyright:
Copyright 2007 Elsevier B.V., All rights reserved.
PY - 2007/5
Y1 - 2007/5
N2 - This paper considers discounted aggregate claims when the claim rates and sizes fluctuate according to the state of the risk business. We provide a system of differential equations for the Laplace-Stieltjes transform of the distribution of discounted aggregate claims under this assumption. Using the differential equations, we present the first two moments of discounted aggregate claims in a Markovian environment. We also derive simple expressions for the moments of discounted aggregate claims when the Markovian environment has two states. Numerical examples are illustrated when the claim sizes are specified.
AB - This paper considers discounted aggregate claims when the claim rates and sizes fluctuate according to the state of the risk business. We provide a system of differential equations for the Laplace-Stieltjes transform of the distribution of discounted aggregate claims under this assumption. Using the differential equations, we present the first two moments of discounted aggregate claims in a Markovian environment. We also derive simple expressions for the moments of discounted aggregate claims when the Markovian environment has two states. Numerical examples are illustrated when the claim sizes are specified.
KW - Circumstance process
KW - Discounted aggregate claims
KW - Laplace-Stieltjes transform
KW - Moments
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U2 - 10.1016/j.insmatheco.2006.07.004
DO - 10.1016/j.insmatheco.2006.07.004
M3 - Article
AN - SCOPUS:33847302482
VL - 40
SP - 485
EP - 497
JO - Insurance: Mathematics and Economics
JF - Insurance: Mathematics and Economics
SN - 0167-6687
IS - 3
ER -